When Avi and Barak work together but independently on a comm

Question

When Avi and Barak work together but independently on a common task, it takes them 12 hours to complete it. If, on the other hand, Avi completed the first half of the task and then Barak completed the second half, the task would take 37.5 hours to complete. If Avi works faster than Barak, Avi works what percent faster than Barak?

(A) 75%
(B) 150%
(C) 225%
(D) 300%
(E) 450%

(A) 75%
(B) 150%
(C) 225%
(D) 300%
(E) 450%

Tinytrotter · Answer

I could not think of any other approach except trial & error, so I assumed that the total work units on the task are 600 and when completed in 12 hours, A & B together put up 50 work units per hour.

Now I made assumptions, since A works faster than B - I assumed rate of A & B as 30 and 20. So if A completed 1/2 of the work (i.e. 300 work units) first in 10 hours (300/30) and B completes the remaining work in 15 hours (300/20). But this would not work as total time was 25 hours. I needed to push it more.

Second iteration was rate of A as 40 and B as 10. So A completed his work in 7.5 hours (300/40) - mini eureka moment as I realized 7.5*4 will be 30 and B will take 30 hours matching the equation perfectly. Therefore with the rates of A as 40/hr and B as 10/hr - arrived at the conclusion that A works at a speed which is 300% greater than B.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=88590 --- Harsha GMAT-Club-Forum-qsfkmzcg.png

kevincan · Answer

This is wonderful ! Let the answer choices be your ally in the end

Vivek1707 · Answer

Let total work be 120 units

Let Avi do  x units  per hour and barak do  y units per hour

So 120/(x+y) = 12 i.e  x + y = 10 ....i

Now as per the question

60/x + 60/y = 37.5 | Note 37.5 is 12.5 x 3

So equation becomes 20 (x+y)/xy = 12.5 
 Plug i  ---> you ll get (20 x 10)/ 12.5 = xy hence  xy = 16

So x + y = 10 and xy = 16 i.e x = 8 and y = 2 fits

Hence 8/2 -1 = 3 i.e  300% Answer D

Gaurav015 · Answer

I used a different approach for this. 1/A+1/B = 1/12
A+B/AB = 1/12
We know that A + B = 75 ( time taken to do the whole work individually)
so AB = 900
Using factorization and the hit-and-trial method, I got the values 60 and 15. Put it in the equation and got the answer. 
Is there any easier approach to do this?

kevincan · Answer

It helps to realize that if A and B are both integers, they will both multiples of five, and they will have opposite parities( one will be even and the other will be odd). Neither will be a multiple of 25

When Avi and Barak work together but independently on a comm

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When Avi and Barak work together but independently on a comm

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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